Normalized Solutions for a Quasilinear Schrodinger Choquard Equation with Exponential Critical Growth in \(\mathbb{R^2}\)

In this paper, we are concerned with normalized solutions to the following quasilinear Schrodinger Choquard equation \(\begin{gathered}-\Delta u-u \Delta u^2+\lambda u=\left(I_\alpha * F(u)\right) f(u), \quad \text { in } \mathbb{R}^2, \\\int_{\mathbb{R}^2}|u|^2 d x=a^2,\end{gathered}\) where a > 0, λ ∈ R, α ∈ (0, 2), Iα denotes the Riesz potential, ∗ denotes the convolution opertor, and the nonlinearity f has an exponential critical growth in the sense of Trudinger-Moser inequality. Using Perturbation method and variational methods with Pohozaev manifold, we can avoid the nondifferentiability of the quasilinear term uΔu2 and prove the existence of normalized solutions with some further assumption.